複素数の計算

${\displaystyle {\left(1-i\right)}^{12}}$${\displaystyle ={\left\{\sqrt{2}\left(\cos \left(-\frac{\pi }{4}\right)+i\sin \left(-\frac{\pi }{4}\right)\right)\right\}}^{12}}$

${\displaystyle ={\left(\sqrt{2}\right)}^{12}\left(\cos \left(-\frac{\pi }{4}\times 12\right)+i\sin \left(-\frac{\pi }{4}\times 12\right)\right)}$

${\displaystyle =64\left\{\cos \left(-3\pi \right)+i\sin \left(-3\pi \right)\right\}}$

${\displaystyle =64\left(-1+i\times 0\right)=64\left(-1+0\right)}$

${\displaystyle =-64}$